hello, (I am in maths/ not an engineer)
I am quite comfortable with analysing simple circuits. Now the big ones are boggling. How can they be broken down? Purely from simplification procedures. The effects the analog signals have must ripple through out the whole system. The maths for slightly larger systems tahn demonstrated in the text books is too long.
It seems that the only approach is to have transistors introduced to break up the circuit to have some non linearity of discrete logic for proper modularity of the system. right?
Or if we don't break up the system with transistors, we can only simulate the system on the computer to escape the complex equations(if they can be made).

Most of the time in industry schematics, the sections of the circuit are broken up for you. Some (very few) will even provide a block diagram for you. This is very helpful but is not necessary as you could make up your own block diagram for the circuit in question. Take for example a mobile FM transmitter. The circuit will look very complicated and confusing but if you break up the schematic into "blocks" each with their own function (like AF amplifier, phase modulator, RF driver, Power amp etc.) each of these circuits lends itself to being analyzed but to try and analyze everything as a whole is time consuming and very difficult. Trying thinking of smaller pieces of the whole circuit and redraw that small circuit block with its own power supply and ground then try analyzing the pieces. Hopefully this makes sense to you.